# How many rounds is needed to implementing Schnorr Non-Interactive zero-knowledge protocol

We can use Fiat-Shamir heuristic to replace 3-move Schnorr's protocol with 1-move non-interactive protocol.

When I implement this non-interactive protocol( ref. https://en.wikipedia.org/wiki/Fiat%E2%80%93Shamir_heuristic): That is

Let $$G$$ be a cyclic group with order $$q$$.

Peggy needs to prove that she knows $$x$$ which is the discrete logarithm of $$y =g^x$$ to a fixed base $$g$$.

1. She randomly chooses an element $$v \in [1,q-1]$$ and computes $$t = g^v$$.
2. She computes $$c = H(g,y,t)$$, where $$H$$ is a cryptographic hash function (implementing random oracle).
3. She computes $$r = v-cx \pmod q$$. The proof is the pair $$(t,r)$$.

4. Anyone can check this proof by $$t = g^r \cdot y^c$$.

My question is that:

Assume that Peggy is prover and Victor is verifier. Can Peggy send $$y =g^x$$ and a proof $$(t,r)$$ in the same round?

Or it should be divided it into two rounds:

1. The first round is that Peggy sends $$y=g^x$$ to Victor.
2. The second round is that a proof $$(t,r)$$ to Victor.

Does it arise any risk if we combine two rounds?

Thanks